I'm using Illustrator cs6. I would like to change the dark gray background that surrounds the art board to a step and repeat patterns of our logo. We use screenshots as a means of generating low-res proofs. Having our step and repeat logo pattern as the background would allow us to easily include it in our low-res screenshot proofs. Can I replace the "system file" for the dark gray to our step and repeat pattern?

You cannot change the pateboard to a logo pattern using Illustrataor preferences, but you can make a layer underneath everything and put your logo pattern in there. In layer options you can turn off print and lock the layer if desired.

Is there a preference that would cause that layer to be in every new document?

Not really. If I wanted what you want, here's how I'd do it:

Create a large artboard to serve as your repeating brand background; large enough to fill the screen with the pattern at the desired size. Add your repeating logo artwork and whatever else you want, (background color, etc.).

Now add an artboard within the first, (choose the artboard tool, hold down Shift, click/drag). Get the size and location of the inner artboard where you want it, (centered within the outer one, I would think), and save as a template, (.AIT).

Load the template. Paste or create customer artwork on the inner artboard and take your screenshot.